Geometric Tail Quantile

Problem

For a geometric variable with success probability p, the tail probability is P(X > n) = (1 - p)^n. Return the smallest integer n >= 0 with P(X > n) <= alpha. Return 0 when p = 1 or alpha = 1, and -1 when p is outside (0, 1] or alpha is outside (0, 1].

Hint

Invert the tail with logarithms, then nudge by a step to avoid floating-point edge cases.

Test cases

case 1

in: [0.5,0.5]

expected: 1

case 2

in: [0.5,0.1]

expected: 4

case 3

in: [0.2,0.01]

expected: 21

case 4

in: [1,0.3]

expected: 0

case 5

in: [0.5,0]

expected: -1

Starter codePython

import math


def geometric_tail_quantile(p, alpha):
    # Your code here
    pass

5 test cases · run your code against them in the editor